Block #463,333

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/28/2014, 1:16:29 AM · Difficulty 10.4158 · 6,344,959 confirmations

TWN

Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header

Block Hash

9beafe4f5514829a01d5d8dd41cc44fd2218f6f8b7abae460cefba836b662ffe

View on Chainz ↗

Height

#463,333

Difficulty

10.415816

Transactions

Size

811 B

Version

Bits

0a6a72eb

Nonce

3,650,648

Timestamp

3/28/2014, 1:16:29 AM

Confirmations

6,344,959

Mined by

⛏️ P2SHAGeAA6U3PSxUj1oRvzAVDuiW2gZfoGAq3P

Merkle Root

50a7bec8cb9ff123df32f8cca2a76aca1a306c9d27b6586da417dcc50b7462fd

Transactions (4)

Coinbase2af9dc38749b7c…dba7fffd425a63

1 in → 1 out9.2300 XPM110 B

AGeAA6U3…ZfoGAq3P

0d70c5c5f72d23…5f4999b6f3c10c

1 in → 2 out9.1900 XPM193 B

ATx8iQ8h…XbxyuQRB AdaeCqfh…UCinJ8zD

2359894c71fe25…d48669a9ce279d

1 in → 2 out5.5864 XPM226 B

AKo1DGWh…uibQZQz1 AdcJYSBY…uKDLXNYs

3955d90a98211e…69a93976133025

1 in → 1 out0.1740 XPM191 B

AGXFqSyj…FxquNuxH

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.411 × 10⁹⁸(99-digit number)

14110699354444336324…16000068223994757119

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 — Twin Prime Pair (origin ± 1)

origin − 1

1.411 × 10⁹⁸(99-digit number)

14110699354444336324…16000068223994757119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.411 × 10⁹⁸(99-digit number)

14110699354444336324…16000068223994757121

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

2.822 × 10⁹⁸(99-digit number)

28221398708888672649…32000136447989514239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.822 × 10⁹⁸(99-digit number)

28221398708888672649…32000136447989514241

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

5.644 × 10⁹⁸(99-digit number)

56442797417777345298…64000272895979028479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.644 × 10⁹⁸(99-digit number)

56442797417777345298…64000272895979028481

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

1.128 × 10⁹⁹(100-digit number)

11288559483555469059…28000545791958056959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.128 × 10⁹⁹(100-digit number)

11288559483555469059…28000545791958056961

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

2.257 × 10⁹⁹(100-digit number)

22577118967110938119…56001091583916113919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.257 × 10⁹⁹(100-digit number)

22577118967110938119…56001091583916113921

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★☆☆☆

Rarity

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer

Block #463,333

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